I haven't found any images of Lady Anne's mother, Cynthia, Countess Spencer wearing this tiara (in a very quick search today). I wondered if it might have been the tiara worn by Countess Cynthia at her wedding but, according to the media, Lady Cynthia Hamilton used orange blossom and greenery instead of a tiara.
Lady Cynthia (Countess Spencer) on her wedding day in 1919.